Problem: Simplify the following expression: $q = \dfrac{4x^2 - 40x + 84}{x - 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $4$ , so we can rewrite the expression: $ q =\dfrac{4(x^2 - 10x + 21)}{x - 7} $ Then we factor the remaining polynomial: $x^2 {-10}x + {21} $ ${-7} {-3} = {-10}$ ${-7} \times {-3} = {21}$ $ (x {-7}) (x {-3}) $ This gives us a factored expression: $\dfrac{4(x {-7}) (x {-3})}{x - 7}$ We can divide the numerator and denominator by $(x + 7)$ on condition that $x \neq 7$ Therefore $q = 4(x - 3); x \neq 7$